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The gas phase decomposition of dimethyl ...

The gas phase decomposition of dimethyl ether follows first order kinetics.
`CH_(3)-O-CH_(3)(g)rarrCH_(4)(g)+H_(2)(g)+CO(g)`
The reaction is carried out in a constant volume container at `500^(@)C` and has a half life of `14.5 min`. Initially, only dimethyl ether is present at a pressure `0.40 atm`. What is the total pressure of the system after `12min`? (Assume ideal gas behaviour)

A

0.946 atm

B

0.785 atm

C

0.777 atm

D

0.749 atm

Text Solution

Verified by Experts

The correct Answer is:
D
`CH_(3)OCH_(3)(g) to CH_(4) + H_(2) + CO`
`{:(t=0,0.4 atm,0,0,0),(t=12,0.4-x,x,x,x):}`
total pressure `0.4 -x + x +x=0.4 + 2x` atm
`K =2.303/t log a/(a-x) rArr K= 2.303/12 log 0.4/(0.4-x)`
but `K=0.693/14.5, therefore 0.693/t_(1//2) = 2.303/12 log 0.4/(0.4-x)`
x=0.175 atm
`therefore` Total pressure `=0.4 + 2x = 0.4 + 2 xx 0.175`
=0.75 atm
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